These are too fragmented for an amateur like me to ID. I think the one in photo IMG_1396 is part of a cow radius+ulna (the two are fused together), towards the distal end. Ideally I would handle the specimens, as I'm not very good at estimating size and rotating them in my mind while looking at photos. The other one (IMG_1403) may be half of the distal end of a metacarpal or metatarsal. Or is it a pelvis fragment?

They don't look fossil to me, but it's worth showing them to an expert just in case.

Oh, that's confusing. When you said 'a couple of bones' I thought you mean two. These are all difficult, as they don't show those features useful for an ID. But given the area you found them, they are most likely remains of butchered cattle.

Indeed these are all too worn to identify species as the identifying features have all gone. They aren't fossil and are very commonly found along the Thames foreshore. However, the five whiter fragments towards the top of the image posted 21 June are all clay pipe fragments, not bone.